$\begin{cases}b(1)=15\\\\ b(n)=b(n-1)\cdot (-3) \end{cases}$ What is the $4^{\text{th}}$ term in the sequence?
This is a recursive formula. It tells us that the first term is $15$ and that the common ratio is $-3$. $\begin{aligned} {b(1)}&=15 \\\\ {b(2)}&={b(1)}\cdot (-3)=-45 \\\\ {b(3)}&={b(2)}\cdot (-3)=135 \\\\ {b(4)}&={b(3)}\cdot (-3)=-405 \end{aligned}$ The $4^{\text{th}}$ term is $-405$.